Nonorientable -manifolds with fundamental group of order

Authors:
Ian Hambleton, Matthias Kreck and Peter Teichner

Journal:
Trans. Amer. Math. Soc. **344** (1994), 649-665

MSC:
Primary 57N13; Secondary 57Q20, 57R67

DOI:
https://doi.org/10.1090/S0002-9947-1994-1234481-2

MathSciNet review:
1234481

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Abstract: In this paper we classify nonorientable topological closed 4-manifolds with fundamental group up to homeomorphism. Our results give a complete list of such manifolds, and show how they can be distinguished by explicit invariants including characteristic numbers and the -invariant associated to a normal -structure by the spectral asymmetry of a certain Dirac operator. In contrast to the oriented case, there exist homotopy equivalent nonorientable topological 4-manifolds which are stably homeomorphic (after connected sum with ) but not homeomorphic.

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DOI:
https://doi.org/10.1090/S0002-9947-1994-1234481-2

Article copyright:
© Copyright 1994
American Mathematical Society